MathDB

Points

A, B

, and

C

are on a line in this order. Points

D

and

E

lie on the same side of this line, in such a way that triangles

ABD

and

BCE

are equilateral. The segments

AE

and

CD

intersect in point

S

. Prove that

\angle ASD = 60^o

.
[asy] unitsize(1.5 cm);
pair A, B, C, D, E, S;
A = (0,0); B = (1,0); C = (2.5,0); D = dir(60); E = B + 1.5*dir(60); S = extension(C,D,A,E);
fill(A--B--D--cycle, gray(0.8)); fill(B--C--E--cycle, gray(0.8)); draw(interp(A,C,-0.1)--interp(A,C,1.1)); draw(A--D--B--E--C); draw(A--E); draw(C--D); draw(anglemark(D,S,A,5));
dot("

A

", A, dir(270)); dot("

B

", B, dir(270)); dot("

C

", C, dir(270)); dot("

D

", D, N); dot("

E

", E, N); dot("

S

", S, N); [/asy]

Problem Statement